A218742 a(n) = (39^n - 1)/38.

0, 1, 40, 1561, 60880, 2374321, 92598520, 3611342281, 140842348960, 5492851609441, 214221212768200, 8354627297959801, 325830464620432240, 12707388120196857361, 495588136687677437080, 19327937330819420046121, 753789555901957381798720, 29397792680176337890150081

Offset: 0

Author

M. F. Hasler, Nov 04 2012

Keywords

• nonn
• easy

Comments

Partial sums of powers of 39 (A009983).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600
• Index entries related to partial sums.
• Index entries for linear recurrences with constant coefficients, signature (40,-39).

Crossrefs

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Cf. A009983.

Programs

Magma

[n le 2 select n-1 else 40*Self(n-1) - 39*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

Mathematica

LinearRecurrence[{40, -39}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
(39^Range[0,20]-1)/38 (* Harvey P. Dale, Mar 05 2023 *)

Maxima

A218742(n):=(39^n-1)/38$
makelist(A218742(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=39^n\38

Formula

a(n) = floor(39^n/38).

From Vincenzo Librandi, Nov 07 2012: (Start)

G.f.: x/((1-x)*(1-39*x)).

a(n) = 40*a(n-1) - 39*a(n-2). (End)

E.g.f.: exp(20*x)*sinh(19*x)/19. - Elmo R. Oliveira, Aug 29 2024